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Module-ify

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Frederik Hanghøj Iversen 2018-02-25 14:27:37 +01:00
parent 12dddc2067
commit ce46e0ae7a
1 changed files with 26 additions and 25 deletions
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src/Cat/Category/Properties.agda
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@ -8,13 +8,14 @@ open import Cubical
open import Cat.Category open import Cat.Category
open import Cat.Category.Functor open import Cat.Category.Functor
open import Cat.Categories.Sets
open import Cat.Equality open import Cat.Equality
open Equality.Data.Product open Equality.Data.Product
module _ {ℓ ℓ' : Level} {ℂ : Category ℓ ℓ'} { A B : Category.Object ℂ } {X : Category.Object ℂ} (f : Category.Arrow ℂ A B) where -- Maybe inline into RawCategory"
module _ {ℓa ℓb : Level} (ℂ : Category ℓa ℓb) where
open Category ℂ open Category ℂ
module _ {A B : Category.Object ℂ } {X : Category.Object ℂ} (f : Category.Arrow ℂ A B) where
iso-is-epi : Isomorphism f → Epimorphism {X = X} f iso-is-epi : Isomorphism f → Epimorphism {X = X} f
iso-is-epi (f- , left-inv , right-inv) g₀ g₁ eq = begin iso-is-epi (f- , left-inv , right-inv) g₀ g₁ eq = begin
g₀ ≡⟨ sym (proj₁ isIdentity) ⟩ g₀ ≡⟨ sym (proj₁ isIdentity) ⟩